The curves for P.E. (U) K.E. (Ek) of two particle system as...

The curves for P.E. (U) K.E. (Ek) of two particle system as shown in figure. At what points system will be bound.
(A) Only at point D
(B) Only at point $\mathrm{A}$
(C) At point $\mathrm{D}$ and $\mathrm{A}$
(D) At points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$

Key Concepts

Energy Conservation

The conservation of energy principle states that the total energy (the sum of kinetic and potential energies) remains constant in an isolated system. This principle is fundamental in understanding how the energy changes between kinetic and potential forms and is essential in analyzing the conditions under which a system remains bound.

Kinetic Energy

Kinetic energy is the energy associated with the movement of the particles. In energy diagrams, the distribution of kinetic energy complements the potential energy so that the total energy remains conserved. When analyzing bound states, points where the kinetic energy approaches zero are often significant, as they might indicate turning points in the motion of the particles.

Energy Diagrams

Energy diagrams graphically represent the variations of kinetic and potential energies as functions of a system parameter, such as the separation between particles. By examining these diagrams, one can identify regions of stable binding (usually at the minima of the potential energy curve) and determine critical points where transitions occur, ultimately providing insight into the dynamic behavior and stability of the system.

Bound State

A bound state refers to a configuration in which two particles remain confined to each other due to their potential energy being lower than the energy required for them to escape. In such a state, the overall energy of the system is negative (or below the dissociation threshold), ensuring that the particles cannot separate indefinitely.

Potential Energy

Potential energy characterizes the energy stored within the system as a function of the relative positions of particles. In two-particle systems, the shape of the potential energy curve indicates attractive or repulsive interactions, and regions where the potential energy is at a minimum signify stable or bound configurations.

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